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Question

In the system shown, mass of block A, B and C are mA=4m, mB=3m and mC=8m. If the system is released from rest, find the acceleration of block B. Assume all surfaces to be smooth and string inextensible.


A
g8
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B
g2
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C
g4
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D
g
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Solution

The correct option is B g2
Let the given system is reframed as shown
So, from the FBDs of A,B and C, we get

T=3maB ... (1)

In vertical direction: 4mgT=4maA ... (2)
In horizontal direction: N2N1=4maC ... (3)
N1+TN2=8maC ... (4)

From constrained condition, using method of intercept we have

..L1+..L2=0aAaCaB=0
aA=aC+aB ... (5)
Adding eq (2) and (3), we get,
4mgT+N2N1=4m(aA+aC)
Using eq. (4), we get
4mg8maC=4m(aA+aC)
4mg=4m(aA+aC+2aC)
aA+3aC=g ... (6)
From (3) & (4), we get
T=12maC ... (7)
From (1) & (7) we have,
3maB=12maCaB=4aC ... (8)
From (5), (6) & (7) we have,
g3aC=aC+4aCaC=g8aB=g2

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